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An efficient computational scheme for solving coupled time-fractional Schrödinger equation via cubic B-spline functions

Author

Listed:
  • Afzaal Mubashir Hayat
  • Muhammad Abbas
  • Homan Emadifar
  • Ahmed S M Alzaidi
  • Tahir Nazir
  • Farah Aini Abdullah

Abstract

The time fractional Schrödinger equation contributes to our understanding of complex quantum systems, anomalous diffusion processes, and the application of fractional calculus in physics and cubic B-spline is a versatile tool in numerical analysis and computer graphics. This paper introduces a numerical method for solving the time fractional Schrödinger equation using B-spline functions and the Atangana-Baleanu fractional derivative. The proposed method employs a finite difference scheme to discretize the fractional derivative in time, while a θ-weighted scheme is used to discretize the space directions. The efficiency of the method is demonstrated through numerical results, and error norms are examined at various values of the non-integer parameter, temporal directions, and spatial directions.

Suggested Citation

  • Afzaal Mubashir Hayat & Muhammad Abbas & Homan Emadifar & Ahmed S M Alzaidi & Tahir Nazir & Farah Aini Abdullah, 2024. "An efficient computational scheme for solving coupled time-fractional Schrödinger equation via cubic B-spline functions," PLOS ONE, Public Library of Science, vol. 19(5), pages 1-24, May.
    • Handle: RePEc:plo:pone00:0296909
    DOI: 10.1371/journal.pone.0296909
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    References listed on IDEAS

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    1. Laskin, Nick, 2000. "Fractional market dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 482-492.
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